Maths Assignment 2 (Test Paper Answers) 

1)

   i)  A ∩ B = B

        A U B = A

 ii)

   a) [1, 2]

       A = {x : x ∈ R, 1 ≤ x ≤ 2}

   b) (0, 1]

      B = {x : x ∈ R, 0 < x ≤ 1}

2)

A = {-1, 0, 1, 2, 3}

B = {2, 3, 5, 7}

A U B = {-1, 0, 1, 2, 3, 5, 7}

A ∩ B = {2, 3}

3)

Domain = R

Range = {-1, 0, 1}

4. U = {1, 2, 3, 4, 5, 6}

   A = {2, 3}

   B = {3,4,5}

   A' = {1, 4, 5, 6}

   B' = {1, 2, 6}

   A U B = {2, 3, 4, 5}

  (A U B)' = A'∩B'

  (A U B)' = {1, 6}

   A'∩ B' =  { 1, 6}

  (A U B)' = A'∩B'

   {1, 6} = {1, 6}

5.

i) {-1, 0, 1}

{}, {-1, 0, 1}, {-1}, {0}, {1}, {-1, 0}, {0, 1}, {-1, 1}

ii)

(  x - 3, 21​+y)=(2,3)

x−3=2x=2+3x=5

21​+y=3y=3−21​

y=26−1​y=25​

6 i)  

f(x)=x2−5x+4x2+3x+5​x2−5x+4

2a−b±b2−4ac​​

2−(−5)±52−4×1×4​​25±25−16​​

2

5±9​​=25±3​

2




5+3​=28​=4

25−3​=22​=1

Domain=R−{1,4}

ii) f(x)=⎩⎨⎧​1−x,1,x+1,​x<0x=0x>0​x∣0∣1∣2∣3∣−1∣−2∣−3y∣1∣2∣3∣4∣  2∣3   ∣4

Domain = R

Range = [1, ∞)

7(i) A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

     2x - y = 1

     2x = 1 - y

f = {(1, 1), (2, 3), (3, 5), (4, 7), (5, 9)}

Domain = {1, 2, 3, 4, 5}

Range =  {1, 3, 5, 7, 9}

(ii) f : Z → Z by

f = {(x, y) : y = x - 1,  x, y ∈ N, x ≤ 4}

Domain = {1, 2, 3, 4}

Range =  {0, 1, 2, 3}

8) 

i)7−2xDomain=RRange=R

ii)−∣x∣Domain=RRange=(−∞,0]

iii) [x ]Domain=RRange=Z

iv)2−x​2−x≥0
Domain=(−∞,2]Range=[0,∞)

v)x2−36​x2−36≥0x2≥36
Domain=(−∞,−6]∪[6,∞)Range=[0,∞)

vi) 

4−x2​4−x2≥0
−2≤x≤2Domain=[−2,2]Range=[0,2]

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